Due to the bandwidth and storage limitations medical images are needed to be compressed before transmission and storage. DICOM (Digital Imaging and Communications in Medicine) specification, which is the medical images standard, provides a mechanism for supporting the use of JPEG still image compression standard. In this paper, we explain a method for compressing medical images by PEG standard and propose two methods for JPEG compression. First, because medical images differ from natural images in optical feature, we propose a method to design adaptively the quantization table using spectrum analysis. Second, because medical images have higher pixel depth than natural images do, we propose a method to design Huffman table which considers the probability distribution feature of symbols. Simulation results show the improved performance compared to the quantization table and the adjusted Huffman table of JPEG standard